I have seen a lot of threads like this over the years and I will NOT claim to have approached this one well. Actually probably not well, but here's what happened.
We told the kids what was going on around the 6 month mark when the physical changes started to become obvious. Up until this point, I was not presenting full time but it was getting more frequent. My children are 5 and 8 now, they were 4 and 8. My son (the older) immediately asked, "well what do I call you now", and I asked what he wanted to call me. He said DAD.
A few months later, Dad started to become a problem for me. It was outing me in public because I was now presenting full time aside from work. It was at this time I started pressing on the name issue. My daughter had started calling me mom, which created other issues.
It was and continues to be very important to the children's birth mother that she is mom. I support that, with the knowledge that it is likely that the children will refer to me as mom over time. But for now, everyone has settled on Maddie, which is somewhat common I guess. My (now ex) spouse was pretty adamant I remain dad. At some point it occurred to me that "dad" has a very specific social connotation and meaning that goes beyond just being male. I no longer met the criteria. Dad no longer fit. I found that I had to mourn that loss as much as anyone else did because that was part of my identity as a parent. That was a role that I was used to filling, a name I was used to responding to, and a source of pride as a parent. "My dad did this with me" kinda thing.
Now, I am Maddie. No one knows what that means, so my kids have started to fall back to Mom when talking about me in public, with teachers and with friends. The issue now is this creates some tension with their mother, but she understands why they do it - it is simpler this way. Kids today are used to split families and families with same sex parents. They do not know how to talk about and do not want to talk about "my mom who was my dad". So mom-Jill is easier than Maddie.
There are many folks on these boards and that I have met in person who are still Dad and have no desire to change that. For me this created massive dysphoria and depression that almost caused me to end my life because I did not know how to deal with the sudden, unexpected consequences to me and my kids by me passing as female and being called Dad in public.
Another bit, when my kids/ex spouse/parents stopped calling me dad, the correct pronouns and name started to show up more consistently.